A Cancellation Property for the Direct Product of Graphs
نویسنده
چکیده
Given graphs A, B and C for which A × C ∼= B × C, it is not generally true that A ∼= B. However, it is known that A × C ∼= B × C implies A ∼= B provided that C is non-bipartite, or that there are homomorphisms from A and B to C. This note proves an additional cancellation property. We show that if B and C are bipartite, then A×C ∼= B × C implies A ∼= B if and only if no component of B admits an involution that interchanges its partite sets.
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تاریخ انتشار 2007